Janet Penman Robertson (nee Douglas) - NZ/Lanarkshire

I am looking for family of my grandmother, Janet Penman Robertson, who immigrated to NZ from Scotland with husband James and daughter Isabella between 1909 & 1911. James worked as a coal miner in the South Island of NZ at Burnetts Face/Denniston.Janet left her family and I have no details of her whereabouts.

Janet's parents were Abraham Douglas and Martha Neilson/Nelson who were married 31/12/1877, Overtown.Her grandparents were Abraham Douglas and Janet Penman married abt 12/2/1842 at Old Monkland/Coatbridge. Any information would be appreciated. Barbara Gerrard